Good resources for learning/reviewing complex time propagator formalism

Question

I studied this at the beginning of my graduate degree but have to review it for my graduate exam. If it's not clear I'm talking about the $\beta = \frac{it}{\hbar} $ turning the integral of your propagator into a "partition function" and the ensuing analysis of eigenvalues as poles in the complex plane. I remember this as being a particularly beautiful and powerful approach but one that was difficult to follow the details and keep an intuitive picture of what's going on.

I'd like to find books (or articles or websites) that have a good qualitative and quantitative explanation of what's going on without getting too bogged down with the mathematical details. Shorter is better but not at the expense of clarity.

Answer 1

For a path integral formulation of this technique, I recommend Hagen Kleinert's massive book on path integrals, if you have access to a copy, or Jean Zinn-Justin's book on path integrals, which is shorter and also very good.

Of course the $\beta = i t / \hbar$ technique can be used in other formulations of quantum mechanics, e.g. the standard canonical quantization. The technique you're looking for though goes under the name of euclidean quantum mechanics. Even just a quick search online turned up many potentially useful sources. Take a look and find one really like.